We propose a probabilistic cellular automata model for the spread ofinnovations, rumors, news, etc. in a social system. The local rule used in themodel is outertotalistic, and the range of interaction can vary. When the rangeR of the rule increases, the takeover time for innovation increases andconverges toward its mean-field value, which is almost inversely proportionalto R when R is large. Exact solutions for R=1 and $R=\infty$ (mean-field) arepresented, as well as simulation results for other values of R. The averagelocal density is found to converge to a certain stationary value, which allowsus to obtain a semi-phenomenological solution valid in the vicinity of thefixed point n=1 (for large t).
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